1. Technical Field
The present invention relates generally to a system for measuring and visualizing the full field of deformation behavior of a body in terms of displacement and strain, and more specifically, to a methodology, algorithms and a corresponding set of tools for the data acquisition, digital image processing, field variable approximation or interpolation and visualization of digital images of a deforming body in three dimensions.
2. Background Technology
Beginning in the 1980's, digital imaging has been used to measure the deformation state of deformable material specimens. These displacement measurement methods have gained significant attention the last two decades, because of the great impact of digital imaging evolution. Modern digital cameras provide a cost effective and highly reliable tool for recording and processing images of an experiment using a personal computer. Experimental mechanics have greatly benefited from those capabilities and some methods have been developed for the determination of displacement and strain fields.
Both pure grid methods and digital image correlation methods have been proposed for providing full-field measurements of displacement and strain.
In pure grid methods, a uniform grid is applied to the surface of a specimen, and the measurement of deformation relies on the motion of the grid. These methods rely on specialized methods for application of the uniform grid. It can be difficult to apply a uniform grid to irregularly shaped bodies, and any inaccuracies in the application of the grid are a major source of errors in the measurement of deformation.
Pure grid methods are described in Sevenhuijsen, P. J., “Two simple methods for deformation demonstration and measurement”, Strain, Vol. 17, pp. 20-24 (1981); Parks, V. J., “Strain measurements using grids”, Opt. Eng., Vol. 21, pp. 633-639 (1982); Sevenhuijsen, P. J., “Photonics for deformations”, Proc 5th Int. Congr. On Expt. Mechanics, SESA, Montreal, (June 1984); and Sevenhuijsen, P. J., “The Photonical, Pure Grid Method”, Optics and Lasers in Engineering, Vol. 18, pp. 173-194, (1993).
Digital image correlation methods are described in Peters, W. H., Ranson, W. F., “Digital imaging techniques in experimental stress analysis”, Opt. Eng. Vol. 21, pp. 427-432, (1982); Bruck, H. A., McNeil, S. R., Sutton, M. A., and Peters W. H., “Digital image correlation using Newton-Raphson method of partial differential correction”, Expt. Mech. Vol. 28, pp. 261-267 (1989); and Cheng, P., Sutton, M. A., Schreier, H. W., McNeill, S. R., “Full-field speckle pattern image correlation with B-Spline deformation function”, Expt. Mech., Vol. 42, pp. 344-352, (2002).
The performance of methods based on digital image correlation, which rely on an applied speckle pattern, can be highly sensitive to the application method and on the specimen surface. Schreier, H. W. Sutton, M. A., “Systematic errors in digital image correlation due to undermatched subset shape functions”, Expt. Mech., Vol. 42, pp. 303-310, (2002) discusses the sensitivity of the method to very specific qualitative and quantitative characteristics of the speckle pattern.
Additional grid-based methods are described in Sirkis, J. S., “System response to automated grid methods”, Opt. Eng., Vol. 29, 1485-93, (1990) and Andersen, K., Helsch, R., “Calculation of grating coordinates using correlation filter techniques”, Optik, Vol. 80, pp. 76-79, (1988). U.S. Pat. No. 7,377,181 to Christ, Jr. et al. discloses the use of coded marks.
Bremand, F. and Lagarde, A., “Two methods of large and small strain measurement on a small size area”, Proc. SEM Spring Conf. On Expt. Mechanics, Keystone, Colo., USA, pp. 173-176, (1986) discloses a method of applying a Fourier transform of the grid pattern.
Mesh-free methods are described in Andrianopoulos, N. P., “Full-field displacement measurement of a speckle grid by using a mesh-free deformation function”, Strain, Vol. 42, 265-271, (2006), in Andrianopoulos, N. P. and Iliopoulos, A. P. “Displacements Measurement in Irregularly Bounded Plates Using Mesh Free Methods”, 16th European Conference of Fracture, Alexandroupolis, Greece, Jul. 3-7, 2006.
Two dimensional random-grid mesh-free techniques are disclosed in Andrianopoulos, N. P. and Iliopoulos, A. P., “Strain measurements by a hybrid experimental-numerical method using a mesh-free field function”, Honorary Volume for Professor P. S. Theocaris, Armenian Academy of Sciences, 31-41, (2005) and in Iliopoulos, A. P., Andrianopoulos, N. P., “An Approach to Analyze Errors Introduced in the Random Grid Strain Measurement Method”, Strain, Vol. 46, pp. 258-266, June 2010 (published online November 2008), and in copending patent application Ser. No. 12/793,594 to Michopoulos et al., published as U.S. Patent Publication No. 20100310128, the entire disclosure of which is incorporated herein by reference.
Early development of six degree-of-freedom (DoF) mechatronic technology is described in J. G. Michopoulos, J. C. Hermanson, A. Iliopoulos, “Toward a Recursive Hexapod for the Multidimensional Mechanical Testing of Composites, Proc. ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2010, held 15-18 Aug. 2010. Three dimensional hexapod materials testing machines developed by the Naval Research Laboratory and the USDA Forest Products Laboratory are also described in J. G. Michopoulos, J. C. Hermanson, and T. Furukawa, “Towards the robotic characterization of the constitutive response of composite materials”, Composite Structures, Vol. 86, pp. 154-164, 2008. A recent recursive hexapod materials testing machine is described in U.S. patent application Ser. No. 13/400,170, filed on Aug. 2, 2012, and in J. Michopoulos et al., “Towards a Recursive Hexapod for the Multidimensional Mechanical Testing of Composites”, ASME 2010 Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2010). The entire disclosure of each of these documents is incorporated herein in its entirety.